How to create path/curve tangent to mesh?
The best way to do it is to position the curve approximately in position over the mesh, and then use the shrinkwrap modifier on the curve (I find near project mode to work the best). 

The only trick is that you will probably have to apply the shrinkwrap modifier once you have it positioned the way you want it, if you are using other modifiers that act on the curve object.

If the curve path at this point is not tangent to the mesh, tab into edit mode, select all control points, and then type Ctrl+T to rotate the orientation of all the control points to be oriented at 90 degree to the mesh surface.